Absorption cooling cycles are environmental and can use solar or waste heat for cooling with very small electric power. This work presents exergy analysis of a double effect parallel flow and single effect absorption cooling systems for comparison. A computer program is developed for the thermodynamic properties of lithium bromide-water solutions by the author in FORTRAN codes for the exergy analysis. The double effect parallel flow absorption systems have better advantages than the single effect absorption system. The coefficient performance (COP) and the exergetic coefficient performance (ECOP) of the double effect parallel flow absorption systems are higher than the single cycles. For the double effect cycle COP and ECOP are found as 1.195 and 0.28, and for the single effect cycle COP and ECOP are found as 0.68 and 0.23, respectively. For each component the exergy loss and exergy destruction is calculated. Most of the irreversibilities are found in the evaporator and in the absorber which about 74% for the double effect, and 72% for the single effect of the total irreversibility. It is concluded that the performance of the evaporator and the absorber is crucial for the two cycles. Improving and better design of these two components will directly improve and affect positively the working conditions and the performance of the cycles.